Question 1

Solve for x.
-$$\log _ { x } \frac { 1 } { 3 } = \frac { 1 } { 2 }$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } \right\}$ 
D)  $\{ 2 \}$ 
A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } \right\}$ 
D)  $\{ 2 \}$

Question 2

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-A quantity that grows or decays by the same percent at regular time periods is said to have growth or decay.

Accepted Answer

A)  logarithmic 
B)  common 
C)  exponential 
D)  natural 
A)  logarithmic 
B)  common 
C)  exponential 
D)  natural

Question 3

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\ln 6 \mathrm { x } = 0.6$

Accepted Answer

A)  $\{ 0.3356 \}$ 
B)  $\{ 0.2718 \}$ 
C)  $\{ 0.3037 \}$ 
D)  $\{ 3.6 \}$ 
A)  $\{ 0.3356 \}$ 
B)  $\{ 0.2718 \}$ 
C)  $\{ 0.3037 \}$ 
D)  $\{ 3.6 \}$

Question 4

Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \
F ( x ) = \sqrt { - 2 x - 4 }
\end{array}$$

Accepted Answer

A)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$ 
B)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$ 
C)  $F ( x ) = ( g \circ h ) ( x )$ 
D)  $F ( x ) = ( f \circ h ) ( x )$ 
A)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$ 
B)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$ 
C)  $F ( x ) = ( g \circ h ) ( x )$ 
D)  $F ( x ) = ( f \circ h ) ( x )$

Question 5

Determine whether the function is a one-to-one function.
-$$f = \{ ( - 3,2 ) , ( - 2,2 ) , ( - 1,1 ) , ( 0 , - 8 ) \}$$

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 6

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$3 \log _ { 3 } x + \frac { 1 } { 6 } \log _ { 3 } x - 2 \log _ { 3 } ( x + 1 )$

Accepted Answer

A)  $\log _ { 3 } \frac { \mathrm { x } ^ { 19 / 6 } } { 2 ( \mathrm { x } + 1 ) }$ 
B)  $\frac { 19 } { 6 } \log _ { 3 } \frac { x } { ( x + 1 ) ^ { 2 } }$ 
C)  $\log _ { 3 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$ 
D)  $\log _ { 3 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$ 
A)  $\log _ { 3 } \frac { \mathrm { x } ^ { 19 / 6 } } { 2 ( \mathrm { x } + 1 ) }$ 
B)  $\frac { 19 } { 6 } \log _ { 3 } \frac { x } { ( x + 1 ) ^ { 2 } }$ 
C)  $\log _ { 3 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$ 
D)  $\log _ { 3 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$

Question 7

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
B)  $f ( x ) = - 4 ^ { x }$ 
C)  $f ( x ) = - \left( \frac { 1 } { 4 } \right) ^ { x }$ 
D)  $f ( x ) = 4 ^ { x }$ 
A)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
B)  $f ( x ) = - 4 ^ { x }$ 
C)  $f ( x ) = - \left( \frac { 1 } { 4 } \right) ^ { x }$ 
D)  $f ( x ) = 4 ^ { x }$

Question 8

Find the value of the logarithmic expression.
-$$\log _ { 3 / 2 } \frac { 2 } { 3 }$$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  1 
B)  $- 1$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 2 }$

Question 9

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 60 & 6 & 12 &
\end{array}$

Accepted Answer

A)  $0.9$ 
B)  15 
C)  $42.4$ 
D)  135 
A)  $0.9$ 
B)  15 
C)  $42.4$ 
D)  135

Question 10

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
-$\begin{array}{l|c|c|c|c|c}
\text { Word (input) } & \text { table } & \text { window } & \text { chair } & \text { door } & \text { couch } \
\hline \text { Second Letter (output) } & \mathrm{a} & \mathrm{i} & \mathrm{h} & \mathrm{o} & \mathrm{o}
\end{array}$

Accepted Answer

A)   
B)   
C) $\text { not one-to-one }$ 
D)   
A)   
B)   
C) $\text { not one-to-one }$ 
D)

Question 11

Write as an exponential equation.
-$$\log _ { 3 } \frac { 1 } { 27 } = - 3$$

Accepted Answer

A)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
B)  $3 ^ { 27 } = 3$ 
C)  $3 ^ { - 3 } = \frac { 1 } { 27 }$ 
D)  $\left( \frac { 1 } { 27 } \right) ^ { 3 } = 3$ 
A)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
B)  $3 ^ { 27 } = 3$ 
C)  $3 ^ { - 3 } = \frac { 1 } { 27 }$ 
D)  $\left( \frac { 1 } { 27 } \right) ^ { 3 } = 3$

Question 12

Solve the equation.
-$$\log _ { 7 } ( x + 7 ) = 4$$

Accepted Answer

A)  $\{ 2408 \}$ 
B)  $\{ 21 \}$ 
C)  $\{ 35 \}$ 
D)  $\{ 2394 \}$ 
A)  $\{ 2408 \}$ 
B)  $\{ 21 \}$ 
C)  $\{ 35 \}$ 
D)  $\{ 2394 \}$

Question 13

Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x } - 8$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 14

Graph the function and its inverse on the same set of axes.
-$$f ( x ) = x ^ { 3 } + 2$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

Solve.
-Hector borrows $3750 at a rate of 9% compounded semiannually. Find how much Hector owes at the end of 5 years. Use: $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$. Round to two decimal places.

Accepted Answer

A)  $\$ 5823.64$ 
B)  $\$ 4673.18$ 
C)  $\$ 39,187.50$ 
D)  $\$ 6406.00$ 
A)  $\$ 5823.64$ 
B)  $\$ 4673.18$ 
C)  $\$ 39,187.50$ 
D)  $\$ 6406.00$

Question 16

Use a calculator to approximate the logarithm to four decimal places.
-$\log 4580$

Accepted Answer

A)  $3.6609$ 
B)  $3.6618$ 
C)  $8.4295$ 
D)  $3.6599$ 
A)  $3.6609$ 
B)  $3.6618$ 
C)  $8.4295$ 
D)  $3.6599$

Question 17

Use the power property to rewrite the expression.
-$\log _ { 4 } 3 ^ { - 2 }$

Accepted Answer

A)  $- 2 \log _ { 4 } 3$ 
B)  $- 8 \log 3$ 
C)  $4 \log _ { 2 } 3$ 
D)  $3 \log _ { 4 } 2$ 
A)  $- 2 \log _ { 4 } 3$ 
B)  $- 8 \log 3$ 
C)  $4 \log _ { 2 } 3$ 
D)  $3 \log _ { 4 } 2$

Question 18

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 6 } \frac { x ^ { 4 } } { y ^ { 7 } }$

Accepted Answer

A)  $\frac { 4 } { 7 } \log _ { 6 } \frac { x } { y }$ 
B)  $4 \log _ { 6 } x - 7 \log _ { 6 } y$ 
C)  $4 \log _ { 6 } x + 7 \log _ { 6 } y$ 
D)  $7 \log _ { 6 } y - 4 \log _ { 6 } x$ 
A)  $\frac { 4 } { 7 } \log _ { 6 } \frac { x } { y }$ 
B)  $4 \log _ { 6 } x - 7 \log _ { 6 } y$ 
C)  $4 \log _ { 6 } x + 7 \log _ { 6 } y$ 
D)  $7 \log _ { 6 } y - 4 \log _ { 6 } x$

Question 19

Write as an exponential equation.
-$\log _ { 1 / 4 } 256 = - 4$

Accepted Answer

A)  $( - 4 ) ^ { 1 / 4 } = 256$ 
B)  $\left( \frac { 1 } { 4 } \right) ^ { - 4 } = 256$ 
C)  $256 ^ { 1 / 4 } = 4$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { 4 } = 256$ 
A)  $( - 4 ) ^ { 1 / 4 } = 256$ 
B)  $\left( \frac { 1 } { 4 } \right) ^ { - 4 } = 256$ 
C)  $256 ^ { 1 / 4 } = 4$ 
D)  $\left( \frac { 1 } { 4 } \right) ^ { 4 } = 256$

Question 20

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-A function of the form $f ( x ) = b ^ { x }$ is called $a ( n )$ـــــــــ function if $\mathrm { b } > 0$, $\mathrm { b }$ is not 1 , and $\mathrm { x }$ is a real number.

Accepted Answer

A)  logarithmic 
B)  symmetric 
C)  exponential 
D)  inverse 
A)  logarithmic 
B)  symmetric 
C)  exponential 
D)  inverse

Solve for x. - $\log _ { x } \frac { 1 } { 3 } = \frac { 1 } { 2 }$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln 6 \mathrm { x } = 0.6$

Write the function F(x) as a composition of f, g, or h. - f(x)=+6g(x)=-2xh(x)= F(x)=

Determine whether the function is a one-to-one function. - $f = \{ ( - 3,2 ) , ( - 2,2 ) , ( - 1,1 ) , ( 0 , - 8 ) \}$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $3 \log _ { 3 } x + \frac { 1 } { 6 } \log _ { 3 } x - 2 \log _ { 3 } ( x + 1 )$

The graph of an exponential function is given. Match the graph to one of the following functions. -

Find the value of the logarithmic expression. - $\log _ { 3 / 2 } \frac { 2 } { 3 }$

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. - Original Amount Half-Life (in years) Number of Years Final Amount after x Time Intervals 60 6 12

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - Word (input) table window chair door couch Second Letter (output)

Write as an exponential equation. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

Solve the equation. - $\log _ { 7 } ( x + 7 ) = 4$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x } - 8$

Graph the function and its inverse on the same set of axes. - $f ( x ) = x ^ { 3 } + 2$ $Graph the function and its inverse on the same set of axes. - f ( x ) = x ^ { 3 } + 2$

Solve. -Hector borrows $3750 at a rate of 9% compounded semiannually. Find how much Hector owes at the end of 5 years. Use: $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ . Round to two decimal places.

Use a calculator to approximate the logarithm to four decimal places. - $\log 4580$

Use the power property to rewrite the expression. - $\log _ { 4 } 3 ^ { - 2 }$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 6 } \frac { x ^ { 4 } } { y ^ { 7 } }$

Write as an exponential equation. - $\log _ { 1 / 4 } 256 = - 4$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Exam 9: Exponential and Logarithmic Functions

Solve for x. - log⁡x13=12\log _ { x } \frac { 1 } { 3 } = \frac { 1 } { 2 }logx​31​=21​

Solve the equation for x. Give an approximate solution accurate to four decimal places. - ln⁡6x=0.6\ln 6 \mathrm { x } = 0.6ln6x=0.6